Title: A Finite Element Method for the Approximation of
the Incompressible, Linearized Euler Equations
Authors: Richard S. Falk and Gerard R. Richter
Source: Advances in Computer Method for Partial Differential Equations
VII, R. Vichevetsky, D. Knight and G. Richter (Eds.),
1992, IMACS
Status: Published
Abstract: We present a finite element method for the transient,
linearized, incompressible Euler equations in two space
dimensions. The velocity equations are discretized via the
discontinuous Galerkin method over a space-time mesh of
tetrahedrons. The mesh is assumed to have been constructed in
such a way that the tetrahedrons can be ordered explicitly with
respect to velocity evolution. For $n\ge 0$, the method yields
a discontinuous piecewise polynomial approximation of degree
$n$ for velocity and a continuous approximation of degree $n+1$
for pressure. We derive error estimates of order $h^{n+1/2}$
for velocity and $h^{n-1/2}$ for the pressure gradient.
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Subj. Class.
URL: http://www.math.rutgers.edu/~falk/papers/euler.pdf